King Yao: author of Weighing the Odds in Sports Betting and Weighing the Odds in Hold'em Poker

Tuesday, February 05, 2008

4th and 13

In the first drive of the 3rd Quarter, with about 7 minutes left, the Patriots had the ball at the Giants 31 yard line, 4th down and 13 to go. They decided to go for the first down. Was that the right decision?

I believe Belicheck knows more about this stuff than almost anyone, including me. But it is still fun to analyze it instead of just saying "well, Belicheck always make the right decision." So, let's analyze it. Let's assume there was nothing wrong with Gostkowski. Throughout the post, I'll make a ton of other assumptions also. Changing any of the assumptions may change the evaluation. I don't pretend to think that all of my assumptions are spot on, I may be wrong on some of them. I do think it is useful to detail the process so any adjustments of assumptions can easily be made to give a better answer.

First, how likely was it for Gostkowski to make a 48-yard FG? I estimate 65%. It is tough to get detailed information on FG length, unless one wanted to pour through every boxscore, so this is how I got the estimate:

All NFL kickers this year in 50 yard or longer attempts were 47 for 99 for a 47.5% success rate. This stat was easy to get from NFL.com.

All NFL kickers this year in the 40 to 49 yard range were 201 for 266 for a 75.6% success rate.

I assumed 48 yards was tougher than the 40-49 yard range, but easier than 50+. I also assumed it is easier to kick a long FG in the dome on turf than in an average NFL game. So I picked 65%. Maybe I am off by 5% ... maybe it should be 60% or 70%...but I'll use 65% in this post.

If they miss the FG, the Giants will get the ball on their own 38. They get the ball at the spot it is kicked, which is about 7 yards behind the line of scrimmage. How much is the additional 7 yards worth? I estimate it is worth .7 points. This is just a guess. Let's also assume a blocked punt won't happen.

Now let's see what the value is if NE tries for the first down.First, I will assume they have a 25% chance of completing the first down. This is just a guess.

I'll assume if they don't convert, it is worth 0 points.I'll assume if they make the 4th down, it'll lead to a 65% chance of a TD, 25% chance of a FG and 10% chance of no score. However, if they don't score but do make the first down, it is likely that NYG get the ball deeper in their own field, I'll assume a value of +1 point for the Patriots if they make the 4th down but don't eventually score. They could intercept it and run it back, but on average, I'd estimate they get the ball at a worse position than their own 31.

The numbers:Make 4th: 25%Miss 4th: 75%

If Make 4th:TD: 65%FG: 25%No Score: 10%

If the Patriots do score, to make it simpler, I'll assume the ensuing kickoff gives the Giants the ball at their own 31, which is where the ball is before the 4th down attempt.

That adds up to 5.4 points if they get the first down. If they have a 25% chance of converting the 4th down attempt, then:

Going for it: 25% x 5.4 = +1.35 points

So using these assumptions, I have the value of attempting a FG at 1.7 points, which is greater than the value of going for the first down at 1.35 points. But what if my assumptions are wrong? Let's just change one number....instead of assuming the Pats had a 25% chance of getting a first down, let's assume it is 32%. With that small adjustment, it makes going for it worth +1.73 points, slightly more than going for the FG.

Overall, I think Belicheck made a mistake. Of course, he could still be right, I doubt he'll correct my mistake if he thinks I made one. Some other thoughts:

I don't think the assumption of converting the first down at 25% is too low. Maybe it was for the Patriots in the regular season, but given the way the Pats offense and the Giants defense were playing, 25% seems right. 32% seems way too high.

Even if going for the FG or the first down had equal value, it is better to go for the FG in this position. That's because NE had the lead - 7 to 3, and 3 points makes a difference as a TD from the Giants only ties the game and does not give them the lead. The team that is ahead is willing to reduce variance. Teams that are ahead should be willing to give up a little EV (in terms of total points) if it means reducing variance. Reducing variance brings up the idea of punting.

So what is the EV if the Patriots punted? Let's say on average they get the Giants the ball at their own 10 - only gaining 21 net yards on the punt. How much is that worth? Well, if 7 yards is worth 0.7 points as we used in the missed FG example above, then 21 net yards equals 3 x 0.7 or 2.1 points. Maybe punting was the best option.

Conclusion:

There are a ton of assumptions in this post. Change any of them drastically enough, and the answer may change. Overall, I really do think going for the first down is a mistake in this spot. Punting may not be better than trying for a FG, but I think those are the two options, not going for the first down. If anyone reading this thinks any of the assumptions should be changed, or if there is an error in my thought process, feel free to email me at kingyao@gmail.com I'm hoping for an email from a guy with BB initials, and I don't mean Barry Bonds.